Chapter 7b day4
November 12, 2015
Practice: Find all solutions using your calculator
a) sin2x > 1
b) sin2x < 1
y1 = sin2x -1
(<0)
y1 = sin2x -1
(>0)
c) cos2x + cosx > 1
y1 = cos2x + cosx -1
( > 0)
[ 0,
]
[
,2 )
Chapter 7b day4
November 12, 2015
Chapter 7b day4
November 12, 2015
Trig Chapter 7B day 4
Principal and General Values
(AKA PV's and GV's)
OBJ: Evaluate exact trig expressions for both Principal
and General values (solutions)
Principal values: only one angle and it's the angle the
calculator would give, but don't use your calculator.
π
Recall where the calculator
"looks" for trig values:
A
[-
π
π
2, 2]
PV [0,π]
tan-1
sin-1-1
csc
cos-1
cot-1
sec-1
2
cos-1 + csc-1 +
sin-1 + sec-1 +
cos-1 -
π
cot-1 -
-1
tan-1 + cot +
sec-1 -
sin-1 tan-1 csc-1 -
- π2
0
(negative angle)
General solution: all solutions for one period, +n___∏
What is the period for: sin?
cos?
tan?
cot?
sec?
csc?
Chapter 7b day4
November 12, 2015
Let's look at the number line below.
The intervals for PV are shaded
on the number line.
[
[
tan,sin,csc
- 5π
6
o
-135
o
-o2π
3
o
-45o
o
o
45
2
3
o
o
-180 -150 3π-120 -90 -60 π -30π
-4
-π
- π -π 4 - 6
o
[
0
o
30
60
o
π π π 90
4
6
3
π
2
o
o
135
120o
150o
2π 3π 5π
3 4 6
345 o
225
o 210o
180
[
cos, cot, sec
240o
o
270
o
300
o
330
o
360
2π
Chapter 7b day4
November 12, 2015
Find both principal and general values.
ex:
PV
PV
ex:
GV
GV
Chapter 7b day4
November 12, 2015
PV
sin-1
(-
√2
2
GV
)
PV
GV
ex:
PV
ex:
GV
Chapter 7b day4
November 12, 2015
PV
GV
ex:
PV
GV
ex: cos θ = -
ASSIGN: Day 4 p 484 (1-20)
give both principal and general solutions.
Chapter 7b day4
November 12, 2015
Chapter 7b day4
November 12, 2015
Chapter 7b day4
November 12, 2015